Abstract
We propose the concept of level \(r\) consensus as a useful property of a preference profile which considerably enhances the stability of social choice. This concept involves a weakening of unanimity, the most extreme form of consensus. It is shown that if a preference profile exhibits level \(r\) consensus around a given preference relation, there exists a Condorcet winner. In addition, if the number of individuals is odd the majority relation coincides with the preference relation around which there is such consensus and consequently it is transitive. Furthermore, if the level of consensus is sufficiently strong, the Condorcet winner is chosen by all the scoring rules. Level \(r\) consensus therefore ensures the Condorcet consistency of all scoring rules, thus eliminating the tension between decision rules inspired by ranking-based utilitarianism and the majority rule.
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Acknowledgments
This paper is based on the first chapter of Mahajne’s PhD thesis. We thank an editor and two anonymous referees for their useful comments.
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Mahajne, M., Nitzan, S. & Volij, O. Level \(r\) consensus and stable social choice. Soc Choice Welf 45, 805–817 (2015). https://doi.org/10.1007/s00355-015-0882-7
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DOI: https://doi.org/10.1007/s00355-015-0882-7